API v1 is deprecated and will be turned off on January 1, 2022. Check out the API v2 documentation.

CloudConvert can be used to create ZIP, RAR, TAR, TAR.GZ, TAR.BZ2, TAR.LZO or or 7Z archives.

Therefore use the archive mode parameter, as the following example shows. Please note that the mode parameters needs to be set to archive in both the create process API request and the start process API request (refer to the documentation about the other necassary parameters for starting conversions).